Boccardo L., Croce G. Elliptic Partial Differential Equations

Walter de Gruyter GmbH, Berlin/Boston, Germany, 2014. — 205 p. — (De Gruyter Studies in Mathematics 55) — ISBN: 978-3-11-031540-0.Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason the book is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.Some fixed point theorems
Preliminaries of real analysis
Linear and semilinear elliptic equations
Nonlinear elliptic equations
Summability of the solutions
H2 regularity for linear problems
Spectral analysis for linear operators
Calculus of variations and Euler’s equation
Natural growth problems
Problems with low summable sources
Uniqueness
A problem with polynomial growth
A problem with degenerate coercivity